| 常曲率空间中的具有共形第二基本形式的子流形 |
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| 引用本文： | 莫小欢,周林峰.常曲率空间中的具有共形第二基本形式的子流形[J].数学年刊A辑(中文版),2004(4). |
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| 作者姓名： | 莫小欢 周林峰 |
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| 作者单位： | 北京大学数学科学学院，北京大学数学科学学院 北京 100871，北京 100871 |
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| 基金项目： | 国家自然科学基金(No.10171002) |
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| 摘 要： | 以把调和态射看作等距浸入的单位法投影的问题为背景,研究了具有共形第二基本形式的子流形,论证了具有共形第二基本形式的高维子流形,一般不是由极小点和全脐点构成,这和曲面的情形形成了鲜明的对照。也给出了常曲率空间中具有平行中曲率的奇数维子流形的一个完全分类。
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| 关 键 词： | 共形第二基本形式 子流形 常曲率空间 |
SUBMANIFOLDS WITH CONFORMAL SECOND FUNDAMENTAL FORM IN A CONSTANT CURVATURE SPACE |
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| MO Xiaohuan ZHOU Linfeng.SUBMANIFOLDS WITH CONFORMAL SECOND FUNDAMENTAL FORM IN A CONSTANT CURVATURE SPACE[J].Chinese Annals of Mathematics,2004(4). |
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| Authors: | MO Xiaohuan ZHOU Linfeng |
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| Abstract: | Motivated by some issues which enter into harmonic morphisms as unit normal projections of isometric immersions, this paper studies submanifolds with conformal second fundamental form, and demonstrates that high dimensional submanifolds with conformal second fundamental form, are in general not composed of minimal points and totally umbilical points. This contrasts sharply with the situation in surfaces. The authors also give a complete classification of all odd-dimensional these submanifolds with parallel mean curvature in constant curvature spaces. |
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| Keywords: | Conformal second fundamental form Submanifold Constant curvature space |
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